We find a high prevalence of Europeans giving equal financial transfers to their adult children, regardless of siblings' income differences. This behaviour is sharply different from previously documented for American counterparts and it is not predicted by any conventional model on family transfers. We build a model to explain the motives for European parental transfers which includes concern with fairness and leaves altruism as an additional motive. We show that, in contrast to the prediction of the pure altruism model, parents do not offset income inequality among their children but decide to give equal transfers in order to be "fair". However, the parents might start to give larger transfers to poorer children if the siblings' income inequality becomes unbearable from the parent's view. We find evidence for this behaviour using simulations for parameter's distributions and also microeconomic data of 9 European countries from the Survey of Health, Aging, and Retirement in Europe (SHARE).